library(GSODR)
library(mosaic)
library(tidyverse)
library(pander)
library(DT)
library(ggrepel)
library(plotly)
library(dplyr)
library(ggplot2)
library(maps)
library(tmap)
library(leaflet)
library(htmltools)
library(car)
library(mosaicData)
library(ResourceSelection)
library(reshape2)
library(RColorBrewer)
library(scatterplot3d)
library(readr)
library(prettydoc)
library(knitr)
library(kableExtra)
library(formattable)
library(sf)
library(ggspatial)
library(leaflet.extras)
thefallen <- read_csv("C:/Users/paige/OneDrive/Documents/Fall Semester 2024/MATH 325/Statistics-Notebook-master/Data/Math425PastGrades.csv")
Drop the Midterm score.
thefallen <- thefallen %>%
select(MagicTwoGroups, Midterm, FinalExam)
datatable(thefallen, options = list(pageLength = 5)) %>%
formatStyle(columns = names(thefallen),color= "white") %>%
htmltools::tagList(tags$style(HTML("thead th {color: red !important; font-weight: bold !important; }")))
thewarriorsbeforeme <- lm(FinalExam ~ Midterm + as.factor(MagicTwoGroups) + Midterm:as.factor(MagicTwoGroups), data = thefallen)
summary(thewarriorsbeforeme) %>%
pander()
| Estimate | Std. Error | t value | |
|---|---|---|---|
| (Intercept) | -3.692 | 9.125 | -0.4046 |
| Midterm | 0.7731 | 0.1297 | 5.961 |
| as.factor(MagicTwoGroups)2 | 23.44 | 13.95 | 1.681 |
| Midterm:as.factor(MagicTwoGroups)2 | -0.05078 | 0.1868 | -0.2718 |
| Pr(>|t|) | |
|---|---|
| (Intercept) | 0.6863 |
| Midterm | 1.804e-08 |
| as.factor(MagicTwoGroups)2 | 0.09493 |
| Midterm:as.factor(MagicTwoGroups)2 | 0.7862 |
| Observations | Residual Std. Error | \(R^2\) | Adjusted \(R^2\) |
|---|---|---|---|
| 150 | 17.98 | 0.496 | 0.4857 |
\[\underbrace{Y_i}_\text{Final Exam} = \overbrace{\beta_0}^\text{y - int} + \overbrace{\beta_1}^\text{slope}\underbrace{X_{1i}}_\text{Midterm} + \overbrace{\beta_2}^\text{change in y-int}\underbrace{X_{2i}}_\text{MagicTwoGroups} + \overbrace{\beta_3}^\text{change in slope}\underbrace{X_{1i}X_{2i}}_\text{Midterm:MagicTwoGroups} + \epsilon_i\]
\[Y_i = 9.125 + 0.1297X_i + 13.95X_{2i} -0.05078X_{1i}X_{2i} + \epsilon_i\]
prediction <- data.frame(
Midterm=24,
FinalExam= 37,
label = "Prediction Final Exam Score (Group 2): 37"
)
predi.p <- predict(thewarriorsbeforeme, data.frame(Midterm=24, MagicTwoGroups = "2"), interval= "prediction")
b <- coef(thewarriorsbeforeme)
thefallen$MagicTwoGroups <- as.factor(thefallen$MagicTwoGroups)
warriors.plot <- ggplot(thefallen, aes(y = FinalExam, x = Midterm, color = MagicTwoGroups)) +
geom_point(aes(
text = paste(
"Group:", MagicTwoGroups, "<br>",
"Midterm Score:", Midterm, "<br>",
"Final Exam Score:", FinalExam
)
), size = 1) +
stat_function(fun = function(x) b[1] + b[2]*x, color = "red") +
stat_function(fun = function(x) (b[1] + b[3]) + (b[2] + b[4])*x, color = "darkred") +
scale_color_manual(name = "MagicTwoGroups",
values = c("red", "darkred")) +
labs(title = "Test Performances of MATH 425 BYU-Idaho Students",
x = "Midterm Score",
y="Final Exam Score" ) +
geom_segment(aes(x=24, xend=24, y=predi.p[2], yend=predi.p[3]), alpha = 0.1, color= "pink", lwd = 3) +
geom_point(data=prediction,
aes(x=Midterm, y=FinalExam),
size = 3,
color= "hotpink")+
theme_classic()
ggplotly(warriors.plot, tooltip="text")